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Research Article

Role of π‑electron conjugation in determining the electrical responsive properties of polychlorinated biphenyls: a DFT based computational study

Rakesh Maity1 · Debkumar Mandal1 · Ajay Misra1

Received: 4 June 2019 / Accepted: 17 January 2020 / Published online: 15 February 2020 © Springer Nature Switzerland AG 2020

AbstractGlobal reactivity descriptors e.g. average polarizabilty (αav), chemical hardness (η), electrophilicity index (ω) of some donor–acceptor substituted polychlorinated biphenyl (PCBs) i.e. 2,2′,5,5′-tetrachloro-1,1′-biphenyl (PCB-1a), 2,5,2′,5′-Tetrachloro-4′-dimethylamino-biphenyl-4-carbonitrile (PCB-1b), Dimethyl-(2,5,2′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-1c), 3,3′,5,5′-tetrachloro-1,1′-biphenyl (PCB-2a), 3,5,3′,5′-Tetrachloro-4′-dimethylamino-biphenyl-4-carbonitrile (PCB-2b) and Dimethyl-(3,5,3′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-2c) were computed along the torsional potential of biphenyl ring. Density functional based hybrid functional CAM-B3LYP with 6-31G(d) basis were used to all the computational study. Out of the six compounds, variation of the global reactivity descriptors e.g. αav, η, ω as a function of torsional angle of biphenyl ring, three compounds are not in conformity with the respective optimum principle i.e. minimum polarizability, maximum hardness and minimum electrophilicity principle. In this present research article, we have raised this issue that apart from electronically stable conformation, localization of π-electron plays a major role in determining the optimum values of global reactivity descriptors, αav, η & ω. On the other hand computa-tion of first average hyper polarizability (βav) as a function of torsional angle shows that the variation of βav are in good agreement with the optical gap as well as electronic spatial extent (<R2>) of the conformers of all the six compounds.

Keywords Polarizability · First hyper-polarizability · Chemical hardness · Optical gap · Electronic spatial extent (<R2>)

1 Introduction

Biphenyl is a very interesting molecule for several reasons. In the gaseous phase it exists in twisted conformation, where the conjugation between the phenyl rings is not operative. However, the two rings become coplanar in the crystalline state [1], indicating the change of conforma-tion due to crystal packing force. Polychlorinated biphenyl (PCB), is a class of organo halogen compounds synthesized by the reaction of chlorine with biphenyl. Polychlorinated

biphenyls (PCBs) are industrially important chemicals used in various applications requiring chemical stability and have now become widely dispersed. A typical mixture of PCBs may contain over 100 compounds and is a colourless, viscous liquid. The mixture is relatively insoluble in water, showing stability at high temperatures, and is a good dielectric (electrical insulator). Polychlorinated biphenyls (PCBs) are aromatic, synthetic chemicals and there is no natural abandance in the environment [2–5]. They consist of two linked benzene rings in which some or all of the

Electronic supplementary material The online version of this article (https ://doi.org/10.1007/s4245 2-020-2068-x) contains supplementary material, which is available to authorized users.

* Ajay Misra, ajay@mail.vidyasagar.ac.in | 1Department of Chemistry and Chemical Technology, Vidyasagar University, Midnapore, W.B 721 102, India.

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hydrogen atoms are substituted by chlorine atoms. PCBs are harmful persistent organic pollutants (POPs) which are toxic, persist in the environment, bio accumulate through the food chain and are harmful to human health and the environment [6–13]. Because of the low rotational energy barriers the phenyl torsion in biphenyl displays a unique dependence on the state of aggregation [14, 15]. Hence, the electron affinity of PCBs is considered as an important parameter in understanding their toxic nature [16–18]. Accordingly the calculation of electron affinity of various PCBs has invoked attention in theoretical interests. An important property of PCBs are generally intern resist-ance towards both acids and alkalis and thermally stable. This made them useful as applications, including dielectric fluids in transformers and capacitors, heat transfer fluids, and lubricants [19]. PCBs are relatively insoluble in water, and the solubility decreases with increased chlorination. PCBs are also highly soluble in nonpolar organic solvents and are combustible liquids. The combustion products are more hazardous than the material itself. The numbering system for the PCBs is also shown below. Positions 2, 2′, 6, and 6′ are called ortho positions, positions 3, 3′, 5, and 5′ are called meta positions, and positions 4 and 4′ are called para positions. The benzene rings can rotate freely and the two extreme configurations are planar (the two benzene rings in the same plane) and the nonplanar in which the benzene rings are at a 90° angle to each other. The degree of non-planarity is largely determined by the nature num-ber of substituents in the ortho positions. The substitution in the ortho positions with larger chlorine atoms forces the phenyl rings to rotate out of the planar configura-tion. Three-dimensional structure–property correlations for the prediction of thermodynamic properties of PCBs like the enthalpy of vaporization and enthalpy of subli-mation. Organic molecules having conjugated π-electron network are excellent option since they can be easily syn-thesised and modified chemically and have extremely fast switching time as well as can resist high intensity radia-tion. Nonlinear optical properties of a variety of push–pull phenylenes have been studied extensively. Recently, Arulmozhiraja et al. [9] using density functional theory calculations have obtained structure, potential energy, and torsional barriers for some selected polychlorinated biphenyls. Thus DFT, which has repeatedly been proven to be a reliable methodology, could be utilized to calculate reliable torsional barriers for PCBs [20–25].

As example, 2,2′,5,5′-tetrachloro-1,1′-biphenyl (PCB-1a), 2,5,2′,5′-Tetrachloro-4′-dimethylamino-biphenyl-4-carbonitrile (PCB-1b), Dimethyl-(2,5,2′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-1c), 3,3′,5,5′-tetrachloro-1,1′-biphenyl (PCB-2a), 3,5,3′,5′-Tetrachloro-4′-dimethylamino-biphenyl-4-carbonitrile (PCB-2b) and Dimethyl-(3,5,3′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-2c) have been investigated as a subject of

many experimental and theoretical studies on conformational behaviour, torsional barrier and NLO properties. Two aromatic π-conjugated units connected together by a single bond, produce new composite molecules. Apart from the torsional barriers, the structure and potential energy curve associated with rotation about the C–C single bond of a PCB are of fun-damental research interest. In chlorinated biphenyls, this bal-ance in interactions is still perturbed by the chlorine atoms, which influences the geometrical parameters of biphenyls, specifically the torsional angle between the phenyl rings. However, the torsional angle between two phenyl rings with ortho substitution is nearly 90°. PCBs are known to interact with the cellular components, and hence, the addition and the removal of an electron during the formation of the com-plex are significant events. The electron acceptance as well as electron removal to PCBs lead to changes in the torsional angle of PCBs and hence their geometry. Unlike the distinction between the principles based on general quantum theory, i.e. the Huckel rule, the Woodward–Hoffmann rules, and the max-imum molecular valence principle there are some principles, e.g. the hard-soft acid–base principle, the maximum hardness principle (MHP) and minimum polarisability principle (MPP) are rooted in the density functional theory (DFT) [26, 27]. The MPP was formulated on the basis of the MHP and an inverse relationship between chemical hardness and polarisability was found.

Since the inception of these principles scientists are using these as global reactivity descriptors to study the global minima for any potential surfaces. Our present computational study shows that the variation of these parameters to locate global minimum are not the thumb rule, rather the nature and position of substitution play an important role in determining the global energy minimum conformer.

1.1 Computation details

Chemical hardness (η) has been identified as a useful global reactivity index in atoms, molecules, and clusters. The theoretical definition of chemical hardness has been provided by DFT, as the second derivative of electronic energy with respect to the number of electrons N, for a constant external potential V(r) [28].

Operational schemes for the calculation of chemical hardness are based on a finite difference method and thus,

(1)� =

(

�2E

�N2

)

�(r)

(2)� ≈1

2(I.P−E .A)

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The electrophilicity is an another reactivity descrip-tor which allows quantitative classification of the global electrophilic nature of a molecule within a relative scale. Parr et al. [29] proposed the electrophilicity index as a measure of energy lowering due to maximal electron flow between donor and acceptor. They defined elec-trophilicity index as,

According to this definition, this index measures the propensity of chemical species to accept electrons. A good nucleophile is characterised by lower value of chemical potential (µ), electrophilicity index (ω) and conversely a good electrophile is characterised by a high value of µ,ω. This new reactive index measures the stabilisation in energy when the system acquires an additional electronic charge from the environment.

These global quantities, as well as the mean polaris-ability values (αav), have been found useful and comple-mentary tools for the description of chemical reactivity in connection with minimum polarisability and MHPs. Polar-isabilities are calculated at a wavelength of 1064 nm cor-responding to the Nd: YAG frequency, a wavelength used for many Hyper Rayleigh Scattering experiments [30–32].

The first hyperpolarizability [33] is calculated as

where �i =∑

(�ijj+�jij+�jji)3

; i = x, y, z j = x, y, z

In Density functional theory (DFT), as it is used for com-putational chemistry, the hybrid functional B3LYP appears to offer the greatest contribution in terms of number of applications which has been published. However, it is unsuccessful is a number of important applications, (1) the polarizability of long chains, (2) excitations using time dependent theory (TDDFT) for Rydberg states, and (3) charge transfer (CT) excitations. Our computational study also reveals that DFT with B3LYP hybrid functional largely overestimate αav and βav value of the donor–accep-tor substituted biphenyl. The reason for these failures is understood. At long range the exchange potential behaves as − 0.2r−1 instead of exact value − r−1. Even through, the potential is an improvement over the LDA and BLYP, where there is no r−1 dependence in the potential. On the other hand H. Iikura et al. [34] introduced new hybrid exchange correlation functional using the Coulomb-attenuating method (CAM-B3LYP). This functional is a hybrid functional with improved long range properties. Since the titled com-pounds in this present article are mostly charge transfer in character, we have used DFT based CAM-B3LYP hybrid functional with 6-31G(d) basis is an optimum set of com-putational method for the titled compounds.

(3)� = �2∕2�

�vec(−2�;�,�) =√

�

�2x+ �2

y+ �2

z

�

All computations are carried out by using Gaussian 09 programs [35]. Polychlorobiphenyls are optimized by using coulomb-attenuated hybrid exchange–correla-tion functional, CAM-B3LYP, which includes a mixture of Hartree–Fock exchange and DFT exchange correlation. One split-valence basis sets, 6-31G-(d) are utilized for this purpose. Energy for all the six molecules as a function of tortional angle of phenyl ring are optimized by fixing the dihedral angle and the other co-ordinates are allowed to relax steps of D.A angle scan is taken 10° and the enrgy of each steps are plotted as a function of D.A to get the potential energy curve for all the causes.

2 Results and discussion

In the following sections, we have discussed the struc-tures, torsional barriers, potential energy curves and all other global reactivity parameters for the selected PCBs molecule.

The PCBs were grouped into two categories:

1. PCBs with two chlorine atoms at the 2,5,2′,5′ posi-tions as 2,2′,5,5′-tetrachloro-1,1′-biphenyl (PCB-1a), 2,5,2′,5′-Tetrachloro-4′-dimethylamino-biphenyl-4-carbonitrile (PCB-1b) and Dimethyl-(2,5,2′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-1c).

2. PCBs with two chlorine atoms at the 3,5,3′,5′ posi-tions as 3,3′,5,5′-tetrachloro-1,1′-biphenyl (PCB-2a), 3,5,3′,5′-Tetrachloro-4′-dimethylamino-biphenyl-4-carbonitrile (PCB-2b) and Dimethyl-(3,5,3′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-2c).

2.1 Potential energy

Variation of energy of [(PCB-1a), (PCB-1b) & (PCB-1c)] and [(PCB-2a), (PCB-2b) & (PCB-2c)] as a function of dihedral angle are shown in Fig. 1. It is observed from both the table (S1a, S1b, S1c) and Fig. 1, the conformers having dihedral angle in the range 60°–90° are the stable ones in case of PCB-1a, PCB-1b & PCB-1c. It is the position of substitution of Cl atom at the 5′ position which makes these three con-formers having D.A 60–90° energetically more relaxed and stable.

On the other hand the variation of energy as a function of DA of the phenyl ring for (PCB-2a), (PCB-2b) & (PCB-2c) as shown Fig. 1, illustrate that the conformer with DA 40° are the most stable and that at 90° are the least stable. In this case, the steric hindrance of the Cl atoms has no role on the relative orientation of the phenyl rings and hence similar orientation of the phenyl rings (40°) as that of unsubstituted biphenyl (40°) are obtained in this series of molecules.

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2.2 Polarizability

Variation of average polarizability (αav) as a function of dihedral angle between the two phenyl ring of all the six compounds are shown in Fig. 1. It is observed that both the average polarizability (αav) and energy of PCB-1a, PCB-1b & PCB-1c decreases as the DA varies from planer con-former and reaches their minimum value at DA value ~ 90°. Hence the variations of αav as a function dihedral angle are in conformity with the minimum polarizability prin-ciple. On the other hand, the minimum and maximum energy conformation for PCB-2b & PCB-2c are observed at a dihedral value 40ο and 90ο respectively Fig. 1 and Table (S2a, S2b, S2c). According to MPP, αav should have minimum value when the torsional angle between the two phenyl rings is 40ο and maximum value for perpendicular

conformation. But the observed minimum and maximum value of average polarizability in this series of compounds are found at a dihedral angle 90° and 40° respectively. Thus this series of PCBs shows violation of minimum polariz-ability principle (MPP).

2.3 Chemical hardness

We also computed the chemical hardness (η) of all the conformers, obtained as a function of dihedral angle (DA) between the two phenyl ring. Our computed chemi-cal hardness as a function of dihedral angle are shown in Table-S1a,S1b,S1c & Table-S2a,S2b,S2c and the plot of the same are shown in Fig. 2. Figure 2 illustrate that the value of chemical hardness of PCB-1a, PCB-1b & PCB-1c are maximum where the energies have minimum value.

Fig. 1 Variation of average polarizability and energy versus dihedral angle of PCB-1a, PCB-1b, PCB-1c, PCB-2a, PCB-2b, PCB-2c

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It is found that the 90° conformers of this series of PCB has the minimum energy and maximum hardness value. Thus the variation ‘η’ as a function of dihedral angle between the phenyl rings are in conformity of the maxi-mum hardness principle (MHP). On the other hand, the variation of chemical hardness (η) of PCB-2a, PCB-2b & PCB-2c as a function of dihedral angle between the two phenyl ring (Fig. 2) illustrate the maximum η value at a D.A 90°, though the energy of this series of PCBs show minimum values at DA 40° and maximum energy at 90°. Thus this series of PCBs violates the maximum hardness principle (MHP).

2.4 Electrophilicity index

A good electrophile in this sense is characterised by a high value of chemical potential (μ) and a low value of hardness (η). Variations of electrophilicity (ω) as a function of dihe-dral angle are shown in Fig. 3. In case of all the molecules, electrophilicity (ω) value decreases with the increase of dihedral angle, reaches minimum at the DA value 90ο. It is interesting to note that high electrophilicity values have been obtained for the conformations corresponding to DA = 180° and 0°. The high electrophilicity value can be used as a criterion for the high toxic nature in the case of PCBs. It is clear that ω can be used as a proper descriptor for toxicity in PCBs. We once again devide the PCBs into two class. In case of PCB-1a, PCB-1b & PCB-1c, the value of electrophilicity index reaches minima at their minimum

Fig. 2 Variation of Chemical hardness and energy versus dihedral angle of PCB-1a, PCB-1b, PCB-1c, PCB-2a, PCB-2b, PCB-2c

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energy conformation i.e. at a dihedral angle value of 90°. Thus this series of PCBs supports the minimum electrophi-licity principle as suggested by Par et al. [26] But the other series of PCB i.e. PCB-2a, PCB-2b & PCB-2c have maximum energy conformer at DA value 90° and these conformers have lowest value of ω in their series. Hence these varia-tions of ω are not in conformity of minimum electrophilic-ity principle.

2.5 Global reactivity descriptors and π‑electron density

The above computational results clearly suggested that one series of PCB, where the Cl atom at 2,2′ position imposing strong steric hindrance are in conformity with the global reactivity descriptor as we pass from different conformers with the change in dihedral angle. But the other series where the Cl atoms at 3,3′ & 5,5′ position, the most stable conformers have similar relative orientation as that unsubstituted biphenyl are not in conformity with

Fig. 3 Variation of Electrophilicity and energy versus dihedral angle of PCB-1a, PCB-1b, PCB-1c, PCB-2a, PCB-2b, PCB-2c

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the global reactivity descriptors as we vary the dihedral angle between the two phenyl ring. Interestingly except energy, the variation of all the global reactivity descriptors as a function of dihedral angle show similar trend. Maxi-mum values of chemical hardness (η) are observed at a DA 90° for all the six PCBs studied in this article. On the other hand, the minimum value of average polarizability (αav) and electrophilicity (ω) are observed at DA value of 90° to all the PCBs.

Orientations of phenyl rings in their energy optimized conformers of these two series of molecules are due to extended conjugation through bi-phenyl ring. In case of PCB-1a, PCB-1b & PCB-1c, the two phenyl ring will pre-fer to minimize the steric repulsion of the Cl atoms at 2,2′ position by rotating the phenyl rings with respect to each other by 90°. On the other hand, the other series of PCBs i.e. PCB-2a, PCB-2b, PCB-2c, there is no such strong steric repulsion due to Cl atom. Here the steric repul-sion is due to H-atom is much less compare to Cl at the 2,2′ position and the phenyl rings orients with respect to each other by 40° to minimize the energy. At this 40° orientation, there is still possibility of partial overlap of the pz orbitals of the adjacent carbon atom of the two phenyl ring. This partial conjugation of π-electron

between the two phenyl ring makes the 40° orientation of the PCBs of this series as stable one. In this connec-tion, we have computed the C–C bond distance between the adjacent carbon atom of all the PCBs studied here. Our computed results as given in Scheme 1 shows that the PCBs in the series PCB-2a, PCB-2b, PCB-2c has shorter C–C (~ 1.48 A°) distance compare to the series PCB-1a, PCB-1b & PCB-1c where C–C distance is ~ 1.49 A°. Thus the π-electron conjugation over the two phenyl ring play a major role in determining the 40° conformation as the stable form of PCBs in the series, PCB-2a, PCB-2b, PCB-2c.

HOMO–LUMO electron densities of all the six PCBs are shown in Fig. S1. HOMO electron distribution for 90° con-formations of all the PCBs show that π-electrons are local-ized within one phenyl rings. But at 40° conformations, π-electrons are distributed over the two phenyl ring for all PCBs as shown in Fig. S1. This localization of π-electrons within a single phenyl ring makes the 90° conformation less polarisable, harder and less electrophilic for all the PCBs. Therefore the localization of π-electrons results the optimum values of all the global reactivity descriptors at their 90° conformation.

Scheme 1 Structures and phe-nyl-phenyl C–C bond length of Polychlorinated biphenyls

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2.6 First hyper polarizability

Variations of first hyper polarizability (βav) as a function of torsional angle between the two phenyl rings of all the PCBs molecules are shown in Fig. 4. Maximum val-ues of first hyper polarizability for all the compounds are obtained when the torsional angle in 0ο or 180ο, i.e. the

planer conformation of biphenyl ring. βav for both the series of molecule decreases with the increase of dihe-dral angle value and reaches the minimum at a dihedral value of 90ο. In case of all the PCBs the variations of βav as a function of dihedral angle are inversely proportional to the optical gap (S1-S0) (Table -S1a, S1b, S1c & S2a, S2b, S2c). The effect of substituent (donor–acceptor) on

Fig. 4 Variation of First Hyper polarizability (βav) and electronic spatial extent (<R2>) versus dihedral angle of PCB-1a, PCB-1b, PCB-1c, PCB-2a, PCB-2b, PCB-2c

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NLO response of the PCBs compounds and its effect on the optical gap were highlighted (Fig. 5 and Table-S3). Figure 5 illustrates that the extent of π conjugation is maximum i.e. optical gap has minimum value for planer conformation of all the PCBs and less π conjugation or maximum optical gap is found for the conformations having two phenyl group perpendicular to each other i.e. DA value of 90°. Hence for all the PCBs in this series show maximum βav at DA value 0° and minimum value at DA value 90°.

We also computed electronic spatial extent (<R2>) which is a measure of extent of electronic volume over

the molecule, as a function of dihedral angle. Figure 4 (Table-S1a, S1b, S1c & Table- S2a, S2b, S2c) clearly suggests that the planer conformations of all the six PCBs shows higher <R2> value and it decreases with the increase DA and reaches its minimum value at DA 90° i.e. when the two phenyl ring are perpendicular to each other. Our previous computational study suggests that higher the value of <R2> , higher is the value of βav [36]. Again, the βav value is directly proportional to the extent of charge trans-fer character of the molecule i.e. smaller the optical gap (S1-S0), higher is the charge transfer character and higher is the βav value. Thus the variation of optical gap (S1-S0) and

Fig. 5 Variation of First Hyper polarizability and Optical Gap (S1–S0) versus dihedral angle of PCB-1a, PCB-1b, PCB-1c, PCB-2a, PCB-2b, PCB-2c

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electronic spatial extent(<R2>) explain the variation of βav of all the PCBs as a function of dihedral angle between the two phenyl ring.

Since the first hyper polarizability is a measure of non-linear optical property of the molecule, we have com-pared the βav values of our studied PCBs at their minimum energy conformations and it is shown in Fig. 6. Our study revealed that the donor acceptor containing PCBs showing maximum charge transfer character within the molecule has the higher βav value.

3 Conclusions

Electrical responsive parameters like polarisabilty (αav), chemical hardness (η), electrophilicity (ω) and first hyper polarizability (βav) of donor–acceptor substituted poly-chlorinated biphenyl 2,2′,5,5′-tetrachloro-1,1′-biphenyl (PCB-1a), 2,5,2 ′ ,5 ′-Tetrachloro-4 ′-dimethylamino-biphenyl-4-carbonitrile (PCB-1b), Dimethyl-(2,5,2′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-1c), 3,3′,5,5′-tetrachloro-1,1′-biphenyl (PCB-2a), 3,5,3′,5′-Tetrachloro-4′-dimethylamino-biphenyl-4-carbonitrile (PCB-2b) and Dimethyl-(3,5,3′,5′-tetrachloro-4′-nitro-biphenyl-4-yl)-amine (PCB-2c) have been carried out as a function of torsional angle of the two phenyl rings using DFT-based theory. Here, the six PCBs are devided into two series. In series one the Cl atoms are present in the 2,2′,5,5′ posi-tion of the phenyl ring i.e. PCB-1a, PCB-1b, PCB-1c and on the other series the Cl atom present at 3,3′,5,5′ position. Our computed global reactivity descriptors, η, αav, ω are in conformity with MPP, MHP & MEP for series one PCB. On the other hand the other series of PCBs i.e. PCB-2a, PCB-2b,

PCB-2c do not obey the MPP, MHP & MEP as we vary the dihedral angle between the two phenyl rings. This appar-ent violation of the optimum principle related to global reactivity descriptors have been explained due to partial overlap of pz orbitals of the two adjacent C-atoms which makes the 40° conformer more stable than the 90° con-former. We also computed first hyper polarizability (βav), electronic spatial extent (<R2>) and optical gap (S1-S0) for all the PCBs as a function of dihedral angle. This vari-ation of βav has nicely been explained with the change of <R2> and optical gap as we vary the dihedral angle.

Acknowledgements R. Maity thanks to UGC-BSR for his individual research fellowship. Departmental computational facilities from DST-FIST (Ref. No. SR/FST/CSI-235/2011) and UGC-SAP (Ref. No. F.5- 9/2015/DRS-11 (SAP-11) programs are gratefully acknowledged. We are thankful to USIC, Vidyasagar University for providing Gaussian-09 software.

Compliance with ethical standards

Conflict of interest The authors declare that they have no conflict of interest.

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Fig. 6 Variation of First Hyper polarizability (βav) versus all the PCBs (PCB-1a, PCB-1b, PCB-1c, PCB-2a, PCB-2b, PCB-2c)

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